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This book covers different aspects of umbral calculus and of its
more recent developments. It discusses the technical details in
depth, including its relevant applications. The book has therefore
manyfold scopes to introduce a mathematical tool, not widespread
known as it should be; to present a complete account of the
relevant capabilities through the use of different examples of
applications; to provide a formal bridge between different fields
of research in pure and applied.
This is a book about Mathematics but not a book of Mathematics. It
is an attempt, between the serious and facetious, of conveying the
idea that a mathematical thought is the result of different
experiences, geographical and social factors. Even though it is not
clear when Mathematics had started, it is evident that it had been
used at an early stage of human history and by ancient Babylonians
and Egyptians who have already developed a sophisticated corpus of
mathematical items, which were the workhorse tools in engineering,
navigation, trades and astronomy. The book sweeps across the
mathematical minds of the Greek and Arab traditions, concepts by
Assyro-Babylonians, and ancient Indian Vedic culture. The
mathematical mind has modeled the evolution of societies and has
been modeled by it. It is now in the midst of a great revolution
and it is not clear where it will bring us. The current new epoch
needs new mathematical tools and, above this, a new way of looking
at Mathematics. This book tells the tale of what went on and what
might go on.
The book covers different aspects of mathematical methods for
Physics. It is designed for graduate courses but a part of it can
also be used by undergraduate students. The leitmotiv of the book
is the search for a common mathematical framework for a wide class
of apparently disparate physical phenomena. An important role,
within this respect, is provided by a nonconventional formulation
of special functions and polynomials. The proposed methods simplify
the understanding of the relevant technicalities and yield a
unifying view to their applications in Physics as well as other
branches of science.The chapters are not organized through the
mathematical study of specific problems in Physics, rather they are
suggested by the formalism itself. For example, it is shown how the
matrix formalism is useful to treat ray Optics, atomic systems
evolution, QED, QCD and Feynman diagrams. The methods presented
here are simple but rigorous. They allow a fairly substantive tool
of analysis for a variety of topics and are useful for beginners as
well as the more experienced researchers.
The book covers different aspects of mathematical methods for
Physics. It is designed for graduate courses but a part of it can
also be used by undergraduate students. The leitmotiv of the book
is the search for a common mathematical framework for a wide class
of apparently disparate physical phenomena. An important role,
within this respect, is provided by a nonconventional formulation
of special functions and polynomials. The proposed methods simplify
the understanding of the relevant technicalities and yield a
unifying view to their applications in Physics as well as other
branches of science.The chapters are not organized through the
mathematical study of specific problems in Physics, rather they are
suggested by the formalism itself. For example, it is shown how the
matrix formalism is useful to treat ray Optics, atomic systems
evolution, QED, QCD and Feynman diagrams. The methods presented
here are simple but rigorous. They allow a fairly substantive tool
of analysis for a variety of topics and are useful for beginners as
well as the more experienced researchers.
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